Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
612 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#20269902 | C2 | semidirect |
| 3. C2×#20269899 | C2 | semidirect |
| 4. #27213006 | C2 | semidirect |
| 5. C2×C22⋊C8×C211 | C2 | semidirect |
| 9. C2×#16809962 | C4 | semidirect |
| 60. Dic422 | C22⋊C4 | semidirect |
| 63. D844 | C22⋊C4 | semidirect |
| 115. C211 | #1788 | semidirect |
| 120. C2×C22⋊C8 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16809962 | 2 |
| C2×#20269902 | 2 |
| C2×#20269899 | 2 |
| #27213006 | 2 |
| C2×C22⋊C8×C211 | 2 |
| #1788 | 211 |